Today’s date is 2020-02-06

Contents

Purpose of this document

The purpose of this document is to demonstrate some skills I have got in R during my course of “Programming AI with R” in the MBA Artificial Intelligence and Machine Learning given by FIAP University in 2019.

Built with 3.6.2

CLASS 01 (12/06/2019)

  • Atribuição de Variáveis
  • Checar o ambiente de programacao
## [1] "/Users/arodrigues/Google Drive/FIAP-MBA-8IA/to_git/R"
  • Salvar arquivos

informacao sobre funcoes

## Error in choose.files(): could not find function "choose.files"

instalar pacotes

## Error in contrib.url(repos, "source"): trying to use CRAN without setting a mirror
## Error: package 'ggplot2' is required by 'plotly' so will not be detached
## Removing package from '/Library/Frameworks/R.framework/Versions/3.6/Resources/library'
## (as 'lib' is unspecified)
  • Arredondamento
## [1] 3.14
  • Consultar classe da varia?vel
## [1] "numeric"
  • Teste de visualizacao
##                    mpg cyl disp  hp drat    wt  qsec vs am gear carb
## Mazda RX4         21.0   6  160 110 3.90 2.620 16.46  0  1    4    4
## Mazda RX4 Wag     21.0   6  160 110 3.90 2.875 17.02  0  1    4    4
## Datsun 710        22.8   4  108  93 3.85 2.320 18.61  1  1    4    1
## Hornet 4 Drive    21.4   6  258 110 3.08 3.215 19.44  1  0    3    1
## Hornet Sportabout 18.7   8  360 175 3.15 3.440 17.02  0  0    3    2
## Valiant           18.1   6  225 105 2.76 3.460 20.22  1  0    3    1

  • Atribuicao de vetores
  • Nomeando vetores
##  Wilian Marcelo   Lucas  Rafael 
##      34      25      31      17
## Marcelo 
##      25
  • Matrizes
##      [,1] [,2] [,3]
## [1,]    1    4    7
## [2,]    2    5    8
## [3,]    3    6    9
## [1] 1 2 3
  • Dataframes e seus comandos
##                      mpg cyl  disp  hp drat    wt  qsec vs am gear carb
## Mazda RX4           21.0   6 160.0 110 3.90 2.620 16.46  0  1    4    4
## Mazda RX4 Wag       21.0   6 160.0 110 3.90 2.875 17.02  0  1    4    4
## Datsun 710          22.8   4 108.0  93 3.85 2.320 18.61  1  1    4    1
## Hornet 4 Drive      21.4   6 258.0 110 3.08 3.215 19.44  1  0    3    1
## Hornet Sportabout   18.7   8 360.0 175 3.15 3.440 17.02  0  0    3    2
## Valiant             18.1   6 225.0 105 2.76 3.460 20.22  1  0    3    1
## Duster 360          14.3   8 360.0 245 3.21 3.570 15.84  0  0    3    4
## Merc 240D           24.4   4 146.7  62 3.69 3.190 20.00  1  0    4    2
## Merc 230            22.8   4 140.8  95 3.92 3.150 22.90  1  0    4    2
## Merc 280            19.2   6 167.6 123 3.92 3.440 18.30  1  0    4    4
## Merc 280C           17.8   6 167.6 123 3.92 3.440 18.90  1  0    4    4
## Merc 450SE          16.4   8 275.8 180 3.07 4.070 17.40  0  0    3    3
## Merc 450SL          17.3   8 275.8 180 3.07 3.730 17.60  0  0    3    3
## Merc 450SLC         15.2   8 275.8 180 3.07 3.780 18.00  0  0    3    3
## Cadillac Fleetwood  10.4   8 472.0 205 2.93 5.250 17.98  0  0    3    4
## Lincoln Continental 10.4   8 460.0 215 3.00 5.424 17.82  0  0    3    4
## Chrysler Imperial   14.7   8 440.0 230 3.23 5.345 17.42  0  0    3    4
## Fiat 128            32.4   4  78.7  66 4.08 2.200 19.47  1  1    4    1
## Honda Civic         30.4   4  75.7  52 4.93 1.615 18.52  1  1    4    2
## Toyota Corolla      33.9   4  71.1  65 4.22 1.835 19.90  1  1    4    1
## Toyota Corona       21.5   4 120.1  97 3.70 2.465 20.01  1  0    3    1
## Dodge Challenger    15.5   8 318.0 150 2.76 3.520 16.87  0  0    3    2
## AMC Javelin         15.2   8 304.0 150 3.15 3.435 17.30  0  0    3    2
## Camaro Z28          13.3   8 350.0 245 3.73 3.840 15.41  0  0    3    4
## Pontiac Firebird    19.2   8 400.0 175 3.08 3.845 17.05  0  0    3    2
## Fiat X1-9           27.3   4  79.0  66 4.08 1.935 18.90  1  1    4    1
## Porsche 914-2       26.0   4 120.3  91 4.43 2.140 16.70  0  1    5    2
## Lotus Europa        30.4   4  95.1 113 3.77 1.513 16.90  1  1    5    2
## Ford Pantera L      15.8   8 351.0 264 4.22 3.170 14.50  0  1    5    4
## Ferrari Dino        19.7   6 145.0 175 3.62 2.770 15.50  0  1    5    6
## Maserati Bora       15.0   8 301.0 335 3.54 3.570 14.60  0  1    5    8
## Volvo 142E          21.4   4 121.0 109 4.11 2.780 18.60  1  1    4    2
## [1] "data.frame"
##                    mpg cyl  disp  hp drat    wt  qsec vs am gear carb
## Mazda RX4         21.0   6 160.0 110 3.90 2.620 16.46  0  1    4    4
## Mazda RX4 Wag     21.0   6 160.0 110 3.90 2.875 17.02  0  1    4    4
## Datsun 710        22.8   4 108.0  93 3.85 2.320 18.61  1  1    4    1
## Hornet 4 Drive    21.4   6 258.0 110 3.08 3.215 19.44  1  0    3    1
## Hornet Sportabout 18.7   8 360.0 175 3.15 3.440 17.02  0  0    3    2
## Valiant           18.1   6 225.0 105 2.76 3.460 20.22  1  0    3    1
## Duster 360        14.3   8 360.0 245 3.21 3.570 15.84  0  0    3    4
## Merc 240D         24.4   4 146.7  62 3.69 3.190 20.00  1  0    4    2
## Merc 230          22.8   4 140.8  95 3.92 3.150 22.90  1  0    4    2
## Merc 280          19.2   6 167.6 123 3.92 3.440 18.30  1  0    4    4
##                 mpg cyl  disp  hp drat    wt qsec vs am gear carb
## Porsche 914-2  26.0   4 120.3  91 4.43 2.140 16.7  0  1    5    2
## Lotus Europa   30.4   4  95.1 113 3.77 1.513 16.9  1  1    5    2
## Ford Pantera L 15.8   8 351.0 264 4.22 3.170 14.5  0  1    5    4
## Ferrari Dino   19.7   6 145.0 175 3.62 2.770 15.5  0  1    5    6
## Maserati Bora  15.0   8 301.0 335 3.54 3.570 14.6  0  1    5    8
## Volvo 142E     21.4   4 121.0 109 4.11 2.780 18.6  1  1    4    2
## [1] 11
## [1] 32
##       mpg             cyl             disp             hp       
##  Min.   :10.40   Min.   :4.000   Min.   : 71.1   Min.   : 52.0  
##  1st Qu.:15.43   1st Qu.:4.000   1st Qu.:120.8   1st Qu.: 96.5  
##  Median :19.20   Median :6.000   Median :196.3   Median :123.0  
##  Mean   :20.09   Mean   :6.188   Mean   :230.7   Mean   :146.7  
##  3rd Qu.:22.80   3rd Qu.:8.000   3rd Qu.:326.0   3rd Qu.:180.0  
##  Max.   :33.90   Max.   :8.000   Max.   :472.0   Max.   :335.0  
##       drat             wt             qsec             vs        
##  Min.   :2.760   Min.   :1.513   Min.   :14.50   Min.   :0.0000  
##  1st Qu.:3.080   1st Qu.:2.581   1st Qu.:16.89   1st Qu.:0.0000  
##  Median :3.695   Median :3.325   Median :17.71   Median :0.0000  
##  Mean   :3.597   Mean   :3.217   Mean   :17.85   Mean   :0.4375  
##  3rd Qu.:3.920   3rd Qu.:3.610   3rd Qu.:18.90   3rd Qu.:1.0000  
##  Max.   :4.930   Max.   :5.424   Max.   :22.90   Max.   :1.0000  
##        am              gear            carb      
##  Min.   :0.0000   Min.   :3.000   Min.   :1.000  
##  1st Qu.:0.0000   1st Qu.:3.000   1st Qu.:2.000  
##  Median :0.0000   Median :4.000   Median :2.000  
##  Mean   :0.4062   Mean   :3.688   Mean   :2.812  
##  3rd Qu.:1.0000   3rd Qu.:4.000   3rd Qu.:4.000  
##  Max.   :1.0000   Max.   :5.000   Max.   :8.000
## Error in eval(expr, envir, enclos): cannot open file '/Library/Frameworks/R.framework/Versions/3.6/Resources/library/ggplot2/data/Rdata.rdb': No such file or directory
## Warning in head(diamonds): restarting interrupted promise evaluation
## Error in head(diamonds): cannot open file '/Library/Frameworks/R.framework/Versions/3.6/Resources/library/ggplot2/data/Rdata.rdb': No such file or directory
## Error: You're passing a function as global data.
## Have you misspelled the `data` argument in `ggplot()`
## Warning: restarting interrupted promise evaluation
## Error in eval(expr, envir, enclos): cannot open file '/Library/Frameworks/R.framework/Versions/3.6/Resources/library/ggplot2/data/Rdata.rdb': No such file or directory
## $mpg
## [1] "numeric"
## 
## $cyl
## [1] "numeric"
## 
## $disp
## [1] "numeric"
## 
## $hp
## [1] "numeric"
## 
## $drat
## [1] "numeric"
## 
## $wt
## [1] "numeric"
## 
## $qsec
## [1] "numeric"
## 
## $vs
## [1] "numeric"
## 
## $am
## [1] "numeric"
## 
## $gear
## [1] "numeric"
## 
## $carb
## [1] "numeric"
  • Exercicio final
##      [,1] [,2] [,3] [,4]
## [1,]    2   10   18   26
## [2,]    4   12   20   28
## [3,]    6   14   22   30
## [4,]    8   16   24   32
##      [,1] [,2] [,3] [,4]
## [1,]    2   10   18   26
## [2,]    4   12   20   28
## [3,]    6   14   22   30
## [4,]    8   16   24   32
  • Exercicio final dataframe
## Error in data.frame(row.names = c("L1", "L2", "L3", "L4"), nome_vetor_1 = v1, : object 'v1' not found

CLASS 02 - (27/06/2019)

  • Instalacao mais fácil do R markdown
  • Sequencias
## [1] TRUE
##  [1]  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15
##  [1] 0.00000000 0.09090909 0.18181818 0.27272727 0.36363636 0.45454545
##  [7] 0.54545455 0.63636364 0.72727273 0.81818182 0.90909091 1.00000000
## [1]  8 10
## [1] 1 2 3
## [1] 1 2 3 4 5
  • Repeticao
## [1] 0 0 0 0 0
## [1] 1 2 3 1 2 3 1 2 3
## [1] 1 1 1 2 2 2 3 3 3
## [1] 12 12 12 12
## [1] 1 2 3 1 2 3 1
## [1] 30
## [1] 10  9  8  7  6  5  4
## [1] 3.141593 4.141593 5.141593 6.141593 7.141593 8.141593 9.141593
##  [1]  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
## [26] 26 27 28 29 30
##  [1]  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
## [26] 26 27 28 29 30
##  [1]  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
## [26] 26 27 28 29 30
## [1]  1  2  3 NA
## [1] 1 2 3
## [1] "integer"
## [1] NA
  • Example dataframe
##    Name  Sex Age
## 1  joão male  45
## 2 maria <NA>  NA
## 3 diego male  NA
##       Name   Sex   Age
## [1,] FALSE FALSE FALSE
## [2,] FALSE  TRUE  TRUE
## [3,] FALSE FALSE  TRUE
## [1] 3
## [1] TRUE
  • Subconjunto
    • Vetor
## [1] 1 2 3 4 5 6 7 8 9
## [1] 2 3 4 5
  • Dataframe
##                      mpg cyl  disp  hp drat    wt  qsec vs am gear carb
## Mazda RX4           21.0   6 160.0 110 3.90 2.620 16.46  0  1    4    4
## Mazda RX4 Wag       21.0   6 160.0 110 3.90 2.875 17.02  0  1    4    4
## Datsun 710          22.8   4 108.0  93 3.85 2.320 18.61  1  1    4    1
## Hornet 4 Drive      21.4   6 258.0 110 3.08 3.215 19.44  1  0    3    1
## Hornet Sportabout   18.7   8 360.0 175 3.15 3.440 17.02  0  0    3    2
## Valiant             18.1   6 225.0 105 2.76 3.460 20.22  1  0    3    1
## Duster 360          14.3   8 360.0 245 3.21 3.570 15.84  0  0    3    4
## Merc 240D           24.4   4 146.7  62 3.69 3.190 20.00  1  0    4    2
## Merc 230            22.8   4 140.8  95 3.92 3.150 22.90  1  0    4    2
## Merc 280            19.2   6 167.6 123 3.92 3.440 18.30  1  0    4    4
## Merc 280C           17.8   6 167.6 123 3.92 3.440 18.90  1  0    4    4
## Merc 450SE          16.4   8 275.8 180 3.07 4.070 17.40  0  0    3    3
## Merc 450SL          17.3   8 275.8 180 3.07 3.730 17.60  0  0    3    3
## Merc 450SLC         15.2   8 275.8 180 3.07 3.780 18.00  0  0    3    3
## Cadillac Fleetwood  10.4   8 472.0 205 2.93 5.250 17.98  0  0    3    4
## Lincoln Continental 10.4   8 460.0 215 3.00 5.424 17.82  0  0    3    4
## Chrysler Imperial   14.7   8 440.0 230 3.23 5.345 17.42  0  0    3    4
## Fiat 128            32.4   4  78.7  66 4.08 2.200 19.47  1  1    4    1
## Honda Civic         30.4   4  75.7  52 4.93 1.615 18.52  1  1    4    2
## Toyota Corolla      33.9   4  71.1  65 4.22 1.835 19.90  1  1    4    1
## Toyota Corona       21.5   4 120.1  97 3.70 2.465 20.01  1  0    3    1
## Dodge Challenger    15.5   8 318.0 150 2.76 3.520 16.87  0  0    3    2
## AMC Javelin         15.2   8 304.0 150 3.15 3.435 17.30  0  0    3    2
## Camaro Z28          13.3   8 350.0 245 3.73 3.840 15.41  0  0    3    4
## Pontiac Firebird    19.2   8 400.0 175 3.08 3.845 17.05  0  0    3    2
## Fiat X1-9           27.3   4  79.0  66 4.08 1.935 18.90  1  1    4    1
## Porsche 914-2       26.0   4 120.3  91 4.43 2.140 16.70  0  1    5    2
## Lotus Europa        30.4   4  95.1 113 3.77 1.513 16.90  1  1    5    2
## Ford Pantera L      15.8   8 351.0 264 4.22 3.170 14.50  0  1    5    4
## Ferrari Dino        19.7   6 145.0 175 3.62 2.770 15.50  0  1    5    6
## Maserati Bora       15.0   8 301.0 335 3.54 3.570 14.60  0  1    5    8
## Volvo 142E          21.4   4 121.0 109 4.11 2.780 18.60  1  1    4    2
## [1] 6
## [1] 6 6 4 6 8
##                    mpg cyl disp  hp drat
## Mazda RX4         21.0   6  160 110 3.90
## Mazda RX4 Wag     21.0   6  160 110 3.90
## Datsun 710        22.8   4  108  93 3.85
## Hornet 4 Drive    21.4   6  258 110 3.08
## Hornet Sportabout 18.7   8  360 175 3.15
##                    mpg cyl  hp
## Mazda RX4         21.0   6 110
## Mazda RX4 Wag     21.0   6 110
## Datsun 710        22.8   4  93
## Hornet 4 Drive    21.4   6 110
## Hornet Sportabout 18.7   8 175
##           mpg cyl  hp
## Mazda RX4  21   6 110
## $a
## [1] 1 2 3
## [1] "list"
## [1] 1 2 3
## [1] 1 2 3
## Error in contrib.url(repos, "source"): trying to use CRAN without setting a mirror
## Error in library(sqldf): there is no package called 'sqldf'
## Error in sqldf("select cyl,hp from mtcars"): could not find function "sqldf"
  • Data
## [1] "1990-02-19 07:45:30 -03"
  • Mostra o que está acontecendo por trás
## [1] 635424330
## attr(,"tzone")
## [1] "America/Sao_Paulo"
## $sec
## [1] 30
## 
## $min
## [1] 45
## 
## $hour
## [1] 7
## 
## $mday
## [1] 19
## 
## $mon
## [1] 1
## 
## $year
## [1] 90
## 
## $wday
## [1] 1
## 
## $yday
## [1] 49
## 
## $isdst
## [1] 0
## 
## $zone
## [1] "-03"
## 
## $gmtoff
## [1] NA
## 
## attr(,"tzone")
## [1] "America/Sao_Paulo"
## [1] 1
  • Biblioteca para a gestão de dados de data e tempo
## Error in contrib.url(repos, "source"): trying to use CRAN without setting a mirror
## Error in library(lubridate): there is no package called 'lubridate'
## Error in ymd("20110604"): could not find function "ymd"
## Error in eval(expr, envir, enclos): object 'lub_date1' not found
## [1] "2011-06-04"
## Error in identical(lub_date1, date_1): object 'lub_date1' not found
## Error in dmy("01-02-1988"): could not find function "dmy"
## Error in eval(expr, envir, enclos): object 'lub_date2' not found
  • System
## Error in now(): could not find function "now"
## Error in today(): could not find function "today"
  • Operacoes com data
## Error in eval(expr, envir, enclos): object 'lub_date2' not found
## Error in eval(expr, envir, enclos): object 'lub_date2' not found
## Error in eval(expr, envir, enclos): object 'lub_date3' not found
  • Resolucao do exercicio
## Error in as.duration(260): could not find function "as.duration"
## Error in duration(num = 260, units = "minutes"): could not find function "duration"
## Error in eval(expr, envir, enclos): object 'lub2' not found
## Error in duration(num = 1, units = "days"): could not find function "duration"
## Error in eval(expr, envir, enclos): object 'lub3' not found
## Error in ddays(x = 12): could not find function "ddays"
## Error in eval(expr, envir, enclos): object 'lub4' not found
  • Exercicio BF
## Error in dmy("01-11-2019"): could not find function "dmy"
## Error in eval(expr, envir, enclos): object 'dtentrada' not found
## Error in wday(dtentrada): could not find function "wday"
## Error in wday(dtentrada): could not find function "wday"
## Error in eval(expr, envir, enclos): object 'bf_check' not found
  • Adiconando 3 componentes ao primeiro dia de novembro
## Error in eval(expr, envir, enclos): object 'dtentrada' not found
## Error in eval(expr, envir, enclos): object 'bf' not found

CLASS 03 (17/08/2019)

  • Vetores:
## [1]   334911 19760626      759    96181     7843
## [1]   669822 39521252     1518   192362    15686
## [1]   223274.000 13173750.667      506.000    64120.667     5228.667
## [1] 1.121656e+11 3.904824e+14 5.765870e+05 9.250849e+09 6.151788e+07
## [1] 1.121656e+11 3.904824e+14 5.765870e+05 9.250849e+09 6.151788e+07
## [1] 1.121654e+11 3.904823e+14 5.760810e+05 9.250785e+09 6.151265e+07
## [1]   334911 19760626      759    96181     7843
## [1] 5.608269e+10 1.952412e+14 2.880405e+05 4.625392e+09 3.075632e+07
## [1]     7843    96181      759 19760626   334911
## [1]     7843    96181      759 19760626   334911
  • Como acessar o help:
## Warning in read.dcf(file.path(p, "DESCRIPTION"), c("Package", "Version")):
## cannot open compressed file '/Library/Frameworks/R.framework/Versions/3.6/
## Resources/library/ggplot2/DESCRIPTION', probable reason 'No such file or
## directory'
## Warning in find.package(if (is.null(package)) loadedNamespaces() else package, :
## there is no package called 'ggplot2'
  • Mostrar todas as fun??es do Pacote Base no pop up:
## Error: <text>:2:0: unexpected end of line
## 1: base::
##    ^
  • Matrizes:
    • Usando matriz, todos os dados devem ser do mesmo tipo.
    • No dataframe é possível misturar os tipos de dados.
##      [,1] [,2]
## [1,]    1    5
## [2,]    2    6
## [3,]    3    7
## [4,]    4    8
##      [,1] [,2]
## [1,]    1    2
## [2,]    3    4
## [3,]    5    6
## [4,]    7    8
##              [,1]         [,2]     [,3]         [,4]         [,5]
## [1,]       334911 1.976063e+07    759.0 9.618100e+04     7843.000
## [2,]       669822 3.952125e+07   1518.0 1.923620e+05    15686.000
## [3,]       223274 1.317375e+07    506.0 6.412067e+04     5228.667
## [4,] 112165377921 3.904823e+14 576081.0 9.250785e+09 61512649.000
## [5,]  56082688960 1.952412e+14 288040.5 4.625392e+09 30756324.500
## [6,]         7843 9.618100e+04    759.0 1.976063e+07   334911.000
  • Por default, o byrow é False. Para melhor desempenho, o ideal é omitir esse argumento.
##          [,1]     [,2]         [,3]         [,4]         [,5]     [,6]
## [1,]   334911   669822   223274.000 1.121654e+11 5.608269e+10     7843
## [2,] 19760626 39521252 13173750.667 3.904823e+14 1.952412e+14    96181
## [3,]      759     1518      506.000 5.760810e+05 2.880405e+05      759
## [4,]    96181   192362    64120.667 9.250785e+09 4.625392e+09 19760626
## [5,]     7843    15686     5228.667 6.151265e+07 3.075632e+07   334911
##              [,1]         [,2]     [,3]         [,4]         [,5]
## [1,] 3.349110e+04 1.976063e+06    75.90 9.618100e+03     784.3000
## [2,] 6.698220e+04 3.952125e+06   151.80 1.923620e+04    1568.6000
## [3,] 2.232740e+04 1.317375e+06    50.60 6.412067e+03     522.8667
## [4,] 1.121654e+10 3.904823e+13 57608.10 9.250785e+08 6151264.9000
## [5,] 5.608269e+09 1.952412e+13 28804.05 4.625392e+08 3075632.4500
## [6,] 7.843000e+02 9.618100e+03    75.90 1.976063e+06   33491.1000
##      rating complaints privileges learning raises critical
## [1,]     67         61         45       47     62       80
## [2,]     64         53         53       58     58       67
## [3,]     67         60         47       39     59       74
## [4,]     69         62         57       42     55       63
## [5,]     68         83         83       45     59       77
  • Save Images
  • Mostra os dados em outro tab
  • Mostra oa classe do objeto:
## [1] "data.frame"
  • Mostra a dimensão do objeto. Linhas, Colunas
## [1] 30  7
  • Converte o dataframe em matriz
##    rating complaints privileges learning raises critical advance
## 1      43         51         30       39     61       92      45
## 2      63         64         51       54     63       73      47
## 3      71         70         68       69     76       86      48
## 4      61         63         45       47     54       84      35
## 5      81         78         56       66     71       83      47
## 6      43         55         49       44     54       49      34
## 7      58         67         42       56     66       68      35
## 8      71         75         50       55     70       66      41
## 9      72         82         72       67     71       83      31
## 10     67         61         45       47     62       80      41
## 11     64         53         53       58     58       67      34
## 12     67         60         47       39     59       74      41
## 13     69         62         57       42     55       63      25
## 14     68         83         83       45     59       77      35
## 15     77         77         54       72     79       77      46
## 16     81         90         50       72     60       54      36
## 17     74         85         64       69     79       79      63
## 18     65         60         65       75     55       80      60
## 19     65         70         46       57     75       85      46
## 20     50         58         68       54     64       78      52
## 21     50         40         33       34     43       64      33
## 22     64         61         52       62     66       80      41
## 23     53         66         52       50     63       80      37
## 24     40         37         42       58     50       57      49
## 25     63         54         42       48     66       75      33
## 26     66         77         66       63     88       76      72
## 27     78         75         58       74     80       78      49
## 28     48         57         44       45     51       83      38
## 29     85         85         71       71     77       74      55
## 30     82         82         39       59     64       78      39
##       rating complaints privileges learning raises critical advance
##  [1,]     43         51         30       39     61       92      45
##  [2,]     63         64         51       54     63       73      47
##  [3,]     71         70         68       69     76       86      48
##  [4,]     61         63         45       47     54       84      35
##  [5,]     81         78         56       66     71       83      47
##  [6,]     43         55         49       44     54       49      34
##  [7,]     58         67         42       56     66       68      35
##  [8,]     71         75         50       55     70       66      41
##  [9,]     72         82         72       67     71       83      31
## [10,]     67         61         45       47     62       80      41
## [11,]     64         53         53       58     58       67      34
## [12,]     67         60         47       39     59       74      41
## [13,]     69         62         57       42     55       63      25
## [14,]     68         83         83       45     59       77      35
## [15,]     77         77         54       72     79       77      46
## [16,]     81         90         50       72     60       54      36
## [17,]     74         85         64       69     79       79      63
## [18,]     65         60         65       75     55       80      60
## [19,]     65         70         46       57     75       85      46
## [20,]     50         58         68       54     64       78      52
## [21,]     50         40         33       34     43       64      33
## [22,]     64         61         52       62     66       80      41
## [23,]     53         66         52       50     63       80      37
## [24,]     40         37         42       58     50       57      49
## [25,]     63         54         42       48     66       75      33
## [26,]     66         77         66       63     88       76      72
## [27,]     78         75         58       74     80       78      49
## [28,]     48         57         44       45     51       83      38
## [29,]     85         85         71       71     77       74      55
## [30,]     82         82         39       59     64       78      39
  • Transforma os dados de string para categorias com uma ordem (levels):
##  [1] "F" "M" "F" "M" "F" "M" "F" "M" "F" "M"
##  [1] F M F M F M F M F M
## Levels: F M
  • Exercicio
## Warning in matrix(c(1, 2), ncol = 19, nrow = 19): data length [2] is not a sub-
## multiple or multiple of the number of rows [19]
##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
##  [1,]    1    2    1    2    1    2    1    2    1     2     1     2     1
##  [2,]    2    1    2    1    2    1    2    1    2     1     2     1     2
##  [3,]    1    2    1    2    1    2    1    2    1     2     1     2     1
##  [4,]    2    1    2    1    2    1    2    1    2     1     2     1     2
##  [5,]    1    2    1    2    1    2    1    2    1     2     1     2     1
##  [6,]    2    1    2    1    2    1    2    1    2     1     2     1     2
##  [7,]    1    2    1    2    1    2    1    2    1     2     1     2     1
##  [8,]    2    1    2    1    2    1    2    1    2     1     2     1     2
##  [9,]    1    2    1    2    1    2    1    2    1     2     1     2     1
## [10,]    2    1    2    1    2    1    2    1    2     1     2     1     2
## [11,]    1    2    1    2    1    2    1    2    1     2     1     2     1
## [12,]    2    1    2    1    2    1    2    1    2     1     2     1     2
## [13,]    1    2    1    2    1    2    1    2    1     2     1     2     1
## [14,]    2    1    2    1    2    1    2    1    2     1     2     1     2
## [15,]    1    2    1    2    1    2    1    2    1     2     1     2     1
## [16,]    2    1    2    1    2    1    2    1    2     1     2     1     2
## [17,]    1    2    1    2    1    2    1    2    1     2     1     2     1
## [18,]    2    1    2    1    2    1    2    1    2     1     2     1     2
## [19,]    1    2    1    2    1    2    1    2    1     2     1     2     1
##       [,14] [,15] [,16] [,17] [,18] [,19]
##  [1,]     2     1     2     1     2     1
##  [2,]     1     2     1     2     1     2
##  [3,]     2     1     2     1     2     1
##  [4,]     1     2     1     2     1     2
##  [5,]     2     1     2     1     2     1
##  [6,]     1     2     1     2     1     2
##  [7,]     2     1     2     1     2     1
##  [8,]     1     2     1     2     1     2
##  [9,]     2     1     2     1     2     1
## [10,]     1     2     1     2     1     2
## [11,]     2     1     2     1     2     1
## [12,]     1     2     1     2     1     2
## [13,]     2     1     2     1     2     1
## [14,]     1     2     1     2     1     2
## [15,]     2     1     2     1     2     1
## [16,]     1     2     1     2     1     2
## [17,]     2     1     2     1     2     1
## [18,]     1     2     1     2     1     2
## [19,]     2     1     2     1     2     1
## Error in eval(expr, envir, enclos): object 'm19' not found
## Error in eval(expr, envir, enclos): object 'M191' not found
## Error in eval(expr, envir, enclos): object 'm191' not found
## Error in eval(expr, envir, enclos): object 'M1919' not found
  • Exercicio Multiplicacao de Matrizes
##              [,1]         [,2]         [,3]         [,4]         [,5]
## [1,] 1.121654e+10 3.904823e+13 5.760810e+04 9.250785e+08 6.151265e+06
## [2,] 4.486615e+10 1.561929e+14 2.304324e+05 3.700314e+09 2.460506e+07
## [3,] 4.985128e+09 1.735477e+13 2.560360e+04 4.111460e+08 2.733896e+06
## [4,] 1.258107e+21 1.524765e+28 3.318693e+10 8.557702e+18 3.783806e+14
## [5,] 3.145268e+20 3.811911e+27 8.296733e+09 2.139425e+18 9.459515e+13
## [6,] 6.151265e+06 9.250785e+08 5.760810e+04 3.904823e+13 1.121654e+10
##              [,1]         [,2]         [,3]         [,4]         [,5]
## [1,] 1.121654e+10 3.904823e+13 5.760810e+04 9.250785e+08 6.151265e+06
## [2,] 4.486615e+10 1.561929e+14 2.304324e+05 3.700314e+09 2.460506e+07
## [3,] 4.985128e+09 1.735477e+13 2.560360e+04 4.111460e+08 2.733896e+06
## [4,] 1.258107e+21 1.524765e+28 3.318693e+10 8.557702e+18 3.783806e+14
## [5,] 3.145268e+20 3.811911e+27 8.296733e+09 2.139425e+18 9.459515e+13
## [6,] 6.151265e+06 9.250785e+08 5.760810e+04 3.904823e+13 1.121654e+10
##            rating   complaints   privileges     learning       raises
## [1,] 1.294340e+09 1.074402e+09 1.068553e+09 1.166279e+09 1.172678e+09
## [2,] 2.588680e+09 2.148805e+09 2.137106e+09 2.332559e+09 2.345357e+09
## [3,] 8.628932e+08 7.162683e+08 7.123688e+08 7.775195e+08 7.817855e+08
## [4,] 2.499903e+16 2.070298e+16 2.070114e+16 2.265364e+16 2.265544e+16
## [5,] 1.249951e+16 1.035149e+16 1.035057e+16 1.132682e+16 1.132772e+16
## [6,] 1.392989e+09 1.258578e+09 1.159639e+09 8.509940e+08 1.112704e+09
##          critical
## [1,] 1.357474e+09
## [2,] 2.714949e+09
## [3,] 9.049829e+08
## [4,] 2.617188e+16
## [5,] 1.308594e+16
## [6,] 1.277835e+09
##              [,1]         [,2]     [,3]         [,4]       [,5]
## [1,] 8.748973e+12 3.045763e+16 45161259 723163125077 4826497119
## [2,] 9.758457e+12 3.397197e+16 50325748 806161985314 5375649929
## [3,] 7.683402e+12 2.674804e+16 39683430 635162041971 4240112259
## [4,] 7.795572e+12 2.713853e+16 40260776 644196678138 4298040232
## [5,] 8.356418e+12 2.909094e+16 43196082 690732861266 4610749739
##      [,1] [,2] [,3] [,4] [,5]
## [1,] TRUE TRUE TRUE TRUE TRUE
## [2,] TRUE TRUE TRUE TRUE TRUE
## [3,] TRUE TRUE TRUE TRUE TRUE
## [4,] TRUE TRUE TRUE TRUE TRUE
## [5,] TRUE TRUE TRUE TRUE TRUE
## [6,] TRUE TRUE TRUE TRUE TRUE
## Error in M7 == M8: non-conformable arrays
  • Matrix Transposta
##       rating complaints privileges learning raises critical advance
##  [1,]     43         51         30       39     61       92      45
##  [2,]     63         64         51       54     63       73      47
##  [3,]     71         70         68       69     76       86      48
##  [4,]     61         63         45       47     54       84      35
##  [5,]     81         78         56       66     71       83      47
##  [6,]     43         55         49       44     54       49      34
##  [7,]     58         67         42       56     66       68      35
##  [8,]     71         75         50       55     70       66      41
##  [9,]     72         82         72       67     71       83      31
## [10,]     67         61         45       47     62       80      41
## [11,]     64         53         53       58     58       67      34
## [12,]     67         60         47       39     59       74      41
## [13,]     69         62         57       42     55       63      25
## [14,]     68         83         83       45     59       77      35
## [15,]     77         77         54       72     79       77      46
## [16,]     81         90         50       72     60       54      36
## [17,]     74         85         64       69     79       79      63
## [18,]     65         60         65       75     55       80      60
## [19,]     65         70         46       57     75       85      46
## [20,]     50         58         68       54     64       78      52
## [21,]     50         40         33       34     43       64      33
## [22,]     64         61         52       62     66       80      41
## [23,]     53         66         52       50     63       80      37
## [24,]     40         37         42       58     50       57      49
## [25,]     63         54         42       48     66       75      33
## [26,]     66         77         66       63     88       76      72
## [27,]     78         75         58       74     80       78      49
## [28,]     48         57         44       45     51       83      38
## [29,]     85         85         71       71     77       74      55
## [30,]     82         82         39       59     64       78      39
##            [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
## rating       43   63   71   61   81   43   58   71   72    67    64    67    69
## complaints   51   64   70   63   78   55   67   75   82    61    53    60    62
## privileges   30   51   68   45   56   49   42   50   72    45    53    47    57
## learning     39   54   69   47   66   44   56   55   67    47    58    39    42
## raises       61   63   76   54   71   54   66   70   71    62    58    59    55
## critical     92   73   86   84   83   49   68   66   83    80    67    74    63
## advance      45   47   48   35   47   34   35   41   31    41    34    41    25
##            [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24]
## rating        68    77    81    74    65    65    50    50    64    53    40
## complaints    83    77    90    85    60    70    58    40    61    66    37
## privileges    83    54    50    64    65    46    68    33    52    52    42
## learning      45    72    72    69    75    57    54    34    62    50    58
## raises        59    79    60    79    55    75    64    43    66    63    50
## critical      77    77    54    79    80    85    78    64    80    80    57
## advance       35    46    36    63    60    46    52    33    41    37    49
##            [,25] [,26] [,27] [,28] [,29] [,30]
## rating        63    66    78    48    85    82
## complaints    54    77    75    57    85    82
## privileges    42    66    58    44    71    39
## learning      48    63    74    45    71    59
## raises        66    88    80    51    77    64
## critical      75    76    78    83    74    78
## advance       33    72    49    38    55    39
  • diag
##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
##  [1,]    1    0    0    0    0    0    0    0    0
##  [2,]    0    2    0    0    0    0    0    0    0
##  [3,]    0    0    3    0    0    0    0    0    0
##  [4,]    0    0    0    4    0    0    0    0    0
##  [5,]    0    0    0    0    5    0    0    0    0
##  [6,]    0    0    0    0    0    6    0    0    0
##  [7,]    0    0    0    0    0    0    7    0    0
##  [8,]    0    0    0    0    0    0    0    8    0
##  [9,]    0    0    0    0    0    0    0    0    9
##       [,1] [,2] [,3] [,4] [,5]
##  [1,]    5    0    0    0    0
##  [2,]    0    5    0    0    0
##  [3,]    0    0    5    0    0
##  [4,]    0    0    0    5    0
##  [5,]    0    0    0    0    5
##  [6,]    0    0    0    0    0
##  [7,]    0    0    0    0    0
##  [8,]    0    0    0    0    0
##  [9,]    0    0    0    0    0
## [10,]    0    0    0    0    0

# Matriz Identidade:

## Error in M %*% I = M: could not find function "%*%<-"
  • Solve usado para calcular a Matriz Inversa (M?)
    • Matriz Inversa: \(M %*% M? = I --> O (n^2 + log(n))\) == High CPU intensive
##    rating complaints privileges learning raises
## 21     50         40         33       34     43
## 22     64         61         52       62     66
## 23     53         66         52       50     63
## 24     40         37         42       58     50
## 25     63         54         42       48     66
##    rating complaints privileges learning raises
## 11     64         53         53       58     58
## 12     67         60         47       39     59
## 13     69         62         57       42     55
## 14     68         83         83       45     59
## 15     77         77         54       72     79
## Warning in read.dcf(file.path(p, "DESCRIPTION"), c("Package", "Version")):
## cannot open compressed file '/Library/Frameworks/R.framework/Versions/3.6/
## Resources/library/ggplot2/DESCRIPTION', probable reason 'No such file or
## directory'
## Warning in find.package(if (is.null(package)) loadedNamespaces() else package, :
## there is no package called 'ggplot2'
##                rating complaints privileges  learning     raises
## rating      0.7389616 -0.1158204  0.2187957  1.173421  0.7785334
## complaints -4.6257572 -6.1397730 -8.1338315 -6.403933 -4.3351608
## privileges  6.8562975  7.6917856 12.2993714  7.961175  5.0382583
## learning   -3.3515454 -3.6302589 -5.2339778 -4.925546 -2.9153565
## raises      2.3203939  4.0460887  3.2439410  3.726420  2.9148688
##                rating complaints privileges  learning     raises
## rating      0.7389616 -0.1158204  0.2187957  1.173421  0.7785334
## complaints -4.6257572 -6.1397730 -8.1338315 -6.403933 -4.3351608
## privileges  6.8562975  7.6917856 12.2993714  7.961175  5.0382583
## learning   -3.3515454 -3.6302589 -5.2339778 -4.925546 -2.9153565
## raises      2.3203939  4.0460887  3.2439410  3.726420  2.9148688
  • Carregar BrFlights2
## Error in eval(expr, envir, enclos): object 'BrFlights2' not found
  • Em geral tudo que for numérico não pode ser usado como fator.
  • Não é muito informativo usar estado como fator.

  • Conta as qtdes das variá?veis.

## Error in table(BrFlights2$Pais.Origem): object 'BrFlights2' not found
## Error in eval(expr, envir, enclos): object 'BrFlights2' not found
  • Transformou os strings em factors com levels.
## Error in factor(BrFlights2$Pais.Origem): object 'BrFlights2' not found
## Warning in read.dcf(file.path(p, "DESCRIPTION"), c("Package", "Version")):
## cannot open compressed file '/Library/Frameworks/R.framework/Versions/3.6/
## Resources/library/ggplot2/DESCRIPTION', probable reason 'No such file or
## directory'
## Warning in find.package(if (is.null(package)) loadedNamespaces() else package, :
## there is no package called 'ggplot2'
##    Sexo
## 1     F
## 2     M
## 3     F
## 4     M
## 5     F
## 6     M
## 7     F
## 8     M
## 9     F
## 10    M
## 11    F
## 12    M
## 13    F
## 14    M
## 15    F
## 16    M
## 17    F
## 18    M
## 19    F
## 20    M
##    Sexo Sexo2
## 1     F     F
## 2     M     M
## 3     F     F
## 4     M     M
## 5     F     F
## 6     M     M
## 7     F     F
## 8     M     M
## 9     F     F
## 10    M     M
## 11    F     F
## 12    M     M
## 13    F     F
## 14    M     M
## 15    F     F
## 16    M     M
## 17    F     F
## 18    M     M
## 19    F     F
## 20    M     M
##    Sexo     Sexo2
## 1     F  Feminino
## 2     M Masculino
## 3     F  Feminino
## 4     M Masculino
## 5     F  Feminino
## 6     M Masculino
## 7     F  Feminino
## 8     M Masculino
## 9     F  Feminino
## 10    M Masculino
## 11    F  Feminino
## 12    M Masculino
## 13    F  Feminino
## 14    M Masculino
## 15    F  Feminino
## 16    M Masculino
## 17    F  Feminino
## 18    M Masculino
## 19    F  Feminino
## 20    M Masculino
##  [1] Feminino  Masculino Feminino  Masculino Feminino  Masculino Feminino 
##  [8] Masculino Feminino  Masculino Feminino  Masculino Feminino  Masculino
## [15] Feminino  Masculino Feminino  Masculino Feminino  Masculino
## Levels: Masculino Feminino
##    Sexo Sexo2
## 1     F     2
## 2     M     1
## 3     F     2
## 4     M     1
## 5     F     2
## 6     M     1
## 7     F     2
## 8     M     1
## 9     F     2
## 10    M     1
## 11    F     2
## 12    M     1
## 13    F     2
## 14    M     1
## 15    F     2
## 16    M     1
## 17    F     2
## 18    M     1
## 19    F     2
## 20    M     1
## Error in nrow(BrFlights2): object 'BrFlights2' not found
## Error in eval(expr, envir, enclos): object 'BrFlights2' not found
## Error in eval(expr, envir, enclos): object 'atrasos' not found
  • Amostras e Simulações
    • Há duas familias de numeros aleatorios: uniforme e normal. Gauss analisou que os fenomenos naturais seguem uma dist. normal.
    • Na Familia Uniforme a chance (prob) de um elemento ser escolhido é igual a de todos os outros elementos.
## Warning in read.dcf(file.path(p, "DESCRIPTION"), c("Package", "Version")):
## cannot open compressed file '/Library/Frameworks/R.framework/Versions/3.6/
## Resources/library/ggplot2/DESCRIPTION', probable reason 'No such file or
## directory'
## Warning in find.package(if (is.null(package)) loadedNamespaces() else package, :
## there is no package called 'ggplot2'
## [1] "O" "A" "U" "T" "R" "G" "I" "L" "N"
## [1] "R" "I" "T" "N" "N" "G" "U" "O" "N"
## [1] "N" "T" "L" "G" "O"
##  [1] "A" "O" "O" "G" "O" "I" "A" "N" "U" "I"
  • set.seed – Util para replicacao de teste. Garante o mesmo resultado apesar da aleatoriedade
## [1]  0.59390132  0.91897737  0.78213630  0.07456498 -1.98935170
## [1] -0.08458607  0.84040013 -0.46348277 -0.55083500  0.73604043
## [1] 153   6
##      Ozone           Solar.R           Wind             Temp      
##  Min.   :  1.00   Min.   :  7.0   Min.   : 1.700   Min.   :56.00  
##  1st Qu.: 18.00   1st Qu.:115.8   1st Qu.: 7.400   1st Qu.:72.00  
##  Median : 31.50   Median :205.0   Median : 9.700   Median :79.00  
##  Mean   : 42.13   Mean   :185.9   Mean   : 9.958   Mean   :77.88  
##  3rd Qu.: 63.25   3rd Qu.:258.8   3rd Qu.:11.500   3rd Qu.:85.00  
##  Max.   :168.00   Max.   :334.0   Max.   :20.700   Max.   :97.00  
##  NA's   :37       NA's   :7                                       
##      Month            Day      
##  Min.   :5.000   Min.   : 1.0  
##  1st Qu.:6.000   1st Qu.: 8.0  
##  Median :7.000   Median :16.0  
##  Mean   :6.993   Mean   :15.8  
##  3rd Qu.:8.000   3rd Qu.:23.0  
##  Max.   :9.000   Max.   :31.0  
## 
##   Ozone Solar.R Wind Temp Month Day
## 1    41     190  7.4   67     5   1
## 2    36     118  8.0   72     5   2
## 3    12     149 12.6   74     5   3
## 4    18     313 11.5   62     5   4
## 5    NA      NA 14.3   56     5   5
## 6    28      NA 14.9   66     5   6
##     Ozone Solar.R Wind Temp Month Day
## 148    14      20 16.6   63     9  25
## 149    30     193  6.9   70     9  26
## 150    NA     145 13.2   77     9  27
## 151    14     191 14.3   75     9  28
## 152    18     131  8.0   76     9  29
## 153    20     223 11.5   68     9  30
##  [1]  1  2  3  8  6  4  7  9 10  5
##     Ozone Solar.R Wind Temp Month Day
## 62    135     269  4.1   84     7   1
## 7      23     299  8.6   65     5   7
## 19     30     322 11.5   68     5  19
## 63     49     248  9.2   85     7   2
## 70     97     272  5.7   92     7   9
## 135    21     259 15.5   76     9  12
## 66     64     175  4.6   83     7   5
## 102    NA     222  8.6   92     8  10
## 121   118     225  2.3   94     8  29
## 8      19      99 13.8   59     5   8
##     Ozone Solar.R Wind Temp Month Day
## 107    NA      64 11.5   79     8  15
## 120    76     203  9.7   97     8  28
## 130    20     252 10.9   80     9   7
## 98     66      NA  4.6   87     8   6
## 29     45     252 14.9   81     5  29
## 45     NA     332 13.8   80     6  14
## 127    91     189  4.6   93     9   4
## 41     39     323 11.5   87     6  10
## 67     40     314 10.9   83     7   6
## 121   118     225  2.3   94     8  29
##  [1]  17  44 125  75   5  67  12  41  11 138
##     Ozone Solar.R Wind Temp Month Day
## 151    14     191 14.3   75     9  28
## 10     NA     194  8.6   69     5  10
## 103    NA     137 11.5   86     8  11
## 51     13     137 10.3   76     6  20
## 69     97     267  6.3   92     7   8
## 127    91     189  4.6   93     9   4
## 29     45     252 14.9   81     5  29
## 78     35     274 10.3   82     7  17
## 73     10     264 14.3   73     7  12
## 71     85     175  7.4   89     7  10
  • Poucas vezes usamos o runif ou sample na simulação de dados, a familia uniforme nao é natural (alvo de dardos)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   39.41   69.88   79.17   79.94   90.04  130.52
## [1] 14.37424
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   17.07   69.87   79.91   79.98   90.15  140.94
## [1] 14.9562
  • pnorm
    • Faz o acumulado entre 0–x. Se eu quiser o intervalo x-y, tenho que calcular a diferen?a entre p(0–x) - p(0–y).
## Warning in read.dcf(file.path(p, "DESCRIPTION"), c("Package", "Version")):
## cannot open compressed file '/Library/Frameworks/R.framework/Versions/3.6/
## Resources/library/ggplot2/DESCRIPTION', probable reason 'No such file or
## directory'
## Warning in find.package(if (is.null(package)) loadedNamespaces() else package, :
## there is no package called 'ggplot2'
## [1] 0.1612813
  • Regressao Linear

    • Exercicio
##   [1]  0.34079969 -0.70334030 -0.37953773 -0.74604744 -0.89810733 -0.33479411
##   [7] -0.50137815 -0.17453570  1.80903740 -0.23010497 -1.13041822  0.21598889
##  [13]  1.23223729  1.60935871  0.40155063 -0.27298403 -0.03615234 -0.15031123
##  [19]  3.76881035 -1.65249598 -1.13514510  0.22767017 -0.18331854 -0.41351862
##  [25] -0.43759528 -0.02618435 -0.85983418  0.16654458  1.47549073  0.19542291
##  [31]  0.15942179 -0.72019328 -0.93550254  0.28543230 -0.73923515  0.42914898
##  [37]  2.73398385 -1.33340333  1.86009535  0.24596992 -0.74598942 -1.48413799
##  [43]  0.22204850  0.47782760  0.73119851  0.17210513  1.18669199 -0.35040940
##  [49]  1.14759741  1.35008401  1.11614940  0.20234597  0.11149061 -1.52799033
##  [55]  0.05750731  2.18746007 -0.07095490  1.29299658  0.37687501 -0.81651082
##  [61] -0.07169406 -2.15850547  2.01919496 -0.05012938 -0.28021325  0.31783776
##  [67] -0.96890304 -0.50034234 -0.96092400 -1.59004694  0.37573467  1.02919849
##  [73]  1.22623137  1.04839459  0.16741396  1.13799896  1.05672549 -0.68015871
##  [79] -1.33738964 -1.80310187  0.70097740 -2.04409051 -0.98805538  0.62738221
##  [85] -0.38374189  3.60352286  0.33221058 -1.24505785  0.24736600 -1.40402871
##  [91]  0.90718101 -0.70395328 -1.56977100  0.34531272  0.67993840  1.14271882
##  [97]  0.40591523 -0.91864023  2.29631307 -0.68969735
##   [1] -3.75659775  2.12868800  2.27665488  1.55921463 -1.26408291  0.37685427
##   [7] -1.81937844 -0.27203422  0.45871256 -1.45026436  1.52226183 -0.15895636
##  [13]  3.45498471  0.81040275 -2.80724337  0.13294523  0.61086046  1.74635528
##  [19] -0.05789542  0.26125767  0.15133924  1.57233132 -3.25560339  0.15629099
##  [25] -1.23012637  0.18654976  0.32920774 -2.14635557 -0.75096643 -0.03949354
##  [31]  1.21682699  0.94841711 -3.38184620  1.84229132  1.04052067  0.87119741
##  [37] -0.47713156 -2.16703385  1.56338695 -1.46717388  0.36607988  0.84414514
##  [43] -0.05537081  0.91068011  2.51271079 -2.66212082 -1.77512795 -0.21009780
##  [49] -0.18099061 -3.60214815  1.42049096  0.08042273  0.59671184  2.48660723
##  [55] -0.70738315 -5.70157860  1.75746243 -4.09245356  3.28924385 -0.83720209
##  [61]  1.83277720  0.72168868  4.40938464  1.73074613  2.99381836  1.34295120
##  [67] -2.41623153 -1.08031926 -1.82448003 -2.12824670 -2.30630212  0.61938098
##  [73]  0.23959470  1.23211873 -1.79065837 -3.52168224 -1.29713661  3.33156120
##  [79]  3.66819053 -3.80747097  3.17767331 -1.02635257  1.68242327 -4.04963704
##  [85]  1.71135381  1.06761329  0.10350465 -0.17619227 -1.78551998 -1.36731370
##  [91]  1.89915756 -1.27262398  2.69238555  1.42654310 -0.56445959 -2.77163920
##  [97] -3.05968686 -0.68812366 -2.60297193  0.05389678
##   [1] -2.574998372  1.222007396  2.017579419  0.567119753 -2.560297571
##   [6]  0.207266055 -2.322134749 -0.121105609  4.576787368 -1.410474305
##  [11] -0.238574610  0.773021417  6.419459284  4.529120168 -1.504142116
##  [16]  0.086977157  1.038555776  1.945732814  7.979725278 -2.543734284
##  [21] -1.618950967  2.527671653 -3.122240463 -0.170746256 -1.605316934
##  [26]  0.634181049 -0.890460614 -1.313266418  2.700015025  0.851352287
##  [31]  2.035670567  0.008030544 -4.752851286  2.913155926  0.062050379
##  [36]  2.229495367  5.490836135 -4.333840506  5.783577638 -0.475234033
##  [41] -0.625898968 -1.624130836  0.888726185  2.366335306  4.475107810
##  [46] -1.817910557  1.098256025 -0.410916597  2.614204214 -0.401980128
##  [51]  4.152789756  0.985114679  1.319693057 -0.069373418 -0.092368523
##  [56] -0.826658460  2.115552638 -1.006460405  4.542993862 -1.970223735
##  [61]  2.189389085 -3.095322249  8.947774567  2.130487362  2.933391864
##  [66]  2.478626715 -3.854037620 -1.581003936 -3.246328026 -4.808340581
##  [71] -1.054832784  3.177777964  3.192057438  3.828907917 -0.955830442
##  [76] -0.745684320  1.316314369  2.471243775  1.493411258 -6.913674722
##  [81]  5.079628119 -4.614533581  0.206312505 -2.294872615  1.443870022
##  [86]  8.774659015  1.267925816 -2.166307968 -0.790787968 -3.675371131
##  [91]  4.213519592 -2.180530534  0.052843550  2.617168551  1.295417206
##  [96]  0.013798435 -1.747856399 -2.025404127  2.489654218 -0.825497906
## No scatter mode specifed:
##   Setting the mode to markers
##   Read more about this attribute -> https://plot.ly/r/reference/#scatter-mode
## Warning in read.dcf(file.path(p, "DESCRIPTION"), c("Package", "Version")):
## cannot open compressed file '/Library/Frameworks/R.framework/Versions/3.6/
## Resources/library/ggplot2/DESCRIPTION', probable reason 'No such file or
## directory'
## Warning in find.package(if (is.null(package)) loadedNamespaces() else package, :
## there is no package called 'ggplot2'

CLASS 04 (19/08/2019)

## Error in eval(expr, envir, enclos): object 'BrFlights2' not found
## Error in nrow(BrFlights2): object 'BrFlights2' not found
  • Exercicio 1
## Error in table(BrFlights2$Pais.Origem): object 'BrFlights2' not found
## Error in eval(expr, envir, enclos): object 'BrFlights2' not found
## Error in is.factor(x): object 'BrFlights2' not found
## Error in eval(expr, envir, enclos): object 'BrFlights2' not found
## Error in eval(expr, envir, enclos): object 'BrFlights2' not found
## Error in eval(expr, envir, enclos): object 'BrFlights2' not found
## Error in which.max(BrFlights2$Atrasos): object 'BrFlights2' not found
  • Loop - WHILE
## Error in print(strenght): object 'strenght' not found
  • Exercicio 2
##      Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
## 1949 112 118 132 129 121 135 148 148 136 119 104 118
## 1950 115 126 141 135 125 149 170 170 158 133 114 140
## 1951 145 150 178 163 172 178 199 199 184 162 146 166
## 1952 171 180 193 181 183 218 230 242 209 191 172 194
## 1953 196 196 236 235 229 243 264 272 237 211 180 201
## 1954 204 188 235 227 234 264 302 293 259 229 203 229
## 1955 242 233 267 269 270 315 364 347 312 274 237 278
## 1956 284 277 317 313 318 374 413 405 355 306 271 306
## 1957 315 301 356 348 355 422 465 467 404 347 305 336
## 1958 340 318 362 348 363 435 491 505 404 359 310 337
## 1959 360 342 406 396 420 472 548 559 463 407 362 405
## 1960 417 391 419 461 472 535 622 606 508 461 390 432
## [1] "ts"
##   [1]   112   230   362   491   612   747   895  1043  1179  1298  1402  1520
##  [13]  1635  1761  1902  2037  2162  2311  2481  2651  2809  2942  3056  3196
##  [25]  3341  3491  3669  3832  4004  4182  4381  4580  4764  4926  5072  5238
##  [37]  5409  5589  5782  5963  6146  6364  6594  6836  7045  7236  7408  7602
##  [49]  7798  7994  8230  8465  8694  8937  9201  9473  9710  9921 10101 10302
##  [61] 10506 10694 10929 11156 11390 11654 11956 12249 12508 12737 12940 13169
##  [73] 13411 13644 13911 14180 14450 14765 15129 15476 15788 16062 16299 16577
##  [85] 16861 17138 17455 17768 18086 18460 18873 19278 19633 19939 20210 20516
##  [97] 20831 21132 21488 21836 22191 22613 23078 23545 23949 24296 24601 24937
## [109] 25277 25595 25957 26305 26668 27103 27594 28099 28503 28862 29172 29509
## [121] 29869 30211 30617 31013 31433 31905 32453 33012 33475 33882 34244 34649
## [133] 35066 35457 35876 36337 36809 37344 37966 38572 39080 39541 39931 40363
  • Lista todas variaveis carregadas na memoria
##  [1] "a"             "A"             "ac"            "Age"          
##  [5] "ai"            "air"           "amostra"       "b"            
##  [9] "B"             "b0"            "b1"            "billy"        
## [13] "c"             "C"             "d"             "date_1"       
## [17] "df"            "dia_date"      "dia_texto"     "dia.time1"    
## [21] "dia.time2"     "dt"            "e"             "i"            
## [25] "idades"        "linhas.idx"    "linhas.sample" "lista"        
## [29] "M"             "M0"            "m1"            "M1"           
## [33] "M19"           "m2"            "M2"            "M3"           
## [37] "M4"            "M5"            "M6"            "M7"           
## [41] "M8"            "MT"            "my_seq"        "Name"         
## [45] "peso"          "Sex"           "sexo"          "strength"     
## [49] "vet"           "vet_num"       "vet1"          "vetor_1"      
## [53] "vetor_2"       "vetor_3"       "vetor_4"       "vetor_5"      
## [57] "vetor_6"       "vetor_7"       "vetor_a"       "vetor_b"      
## [61] "vetor_c"       "x"             "y"
  • Exercicio 3
## [1] 3628800
## [1] 3628800

CLASS 05 (26/8/2019)

  • Obtendo dados com o R
  • Obter dados da Internet
  • read.table abre um arquivo e o converte em data.frame
  • Limpar as variaveis
  • Exercicio
  • Pipe
## Error in eval(lhs, parent, parent): object 'starwars' not found
## Error in eval(lhs, parent, parent): object 'starwars' not found
## Error in eval(lhs, parent, parent): object 'starwars' not found
## Error in head(starwars, .): object 'starwars' not found
## Error in eval(lhs, parent, parent): object 'starwars' not found
## Error in eval(lhs, parent, parent): object 'starwars' not found
## Warning in readChar(con, 5L, useBytes = TRUE): cannot open compressed file 'P:/
## 08IA/BrFlights2.RData', probable reason 'No such file or directory'
## Error in readChar(con, 5L, useBytes = TRUE): cannot open the connection
  • Dplyr - Select (Não confunda com select de SQL)
## Error in eval(lhs, parent, parent): object 'starwars' not found
  • Select pode definir nova ordem de colunas e/ou linhas

AzulFlights <- BrFlights2 %>% filter(Companhia.Aerea == “AZUL”) %>%
select(Companhia.Aerea, Cidade.Origem, Cidade.Destino, Situacao.Voo)

## Error in eval(lhs, parent, parent): object 'BrFlights2' not found
  • DPLYR - ARRANGE
## Error: <text>:10:0: unexpected end of input
## 8:           head(100) %>%
## 9:           # View()
##   ^
  • DYPLR - RENAME
## Error in rename(starwars, nome = name, altura = height, massa = mass): object 'starwars' not found
  • DYPLR - Agregacoes
## Error: <text>:26:0: unexpected end of input
## 24:             ) %>%
## 25:           # View()
##    ^

CLASS 06 (16/09/2019)

  • Plots

##   speed dist
## 1     4    2
## 2     4   10
## 3     7    4
## 4     7   22
## 5     8   16
## 6     9   10
##      speed           dist       
##  Min.   : 4.0   Min.   :  2.00  
##  1st Qu.:12.0   1st Qu.: 26.00  
##  Median :15.0   Median : 36.00  
##  Mean   :15.4   Mean   : 42.98  
##  3rd Qu.:19.0   3rd Qu.: 56.00  
##  Max.   :25.0   Max.   :120.00

*Histograma

## Warning in read.dcf(file.path(p, "DESCRIPTION"), c("Package", "Version")):
## cannot open compressed file '/Library/Frameworks/R.framework/Versions/3.6/
## Resources/library/ggplot2/DESCRIPTION', probable reason 'No such file or
## directory'
## Warning in find.package(if (is.null(package)) loadedNamespaces() else package, :
## there is no package called 'ggplot2'

*BoxPlots

##      Ozone           Solar.R           Wind             Temp      
##  Min.   :  1.00   Min.   :  7.0   Min.   : 1.700   Min.   :56.00  
##  1st Qu.: 18.00   1st Qu.:115.8   1st Qu.: 7.400   1st Qu.:72.00  
##  Median : 31.50   Median :205.0   Median : 9.700   Median :79.00  
##  Mean   : 42.13   Mean   :185.9   Mean   : 9.958   Mean   :77.88  
##  3rd Qu.: 63.25   3rd Qu.:258.8   3rd Qu.:11.500   3rd Qu.:85.00  
##  Max.   :168.00   Max.   :334.0   Max.   :20.700   Max.   :97.00  
##  NA's   :37       NA's   :7                                       
##      Month            Day      
##  Min.   :5.000   Min.   : 1.0  
##  1st Qu.:6.000   1st Qu.: 8.0  
##  Median :7.000   Median :16.0  
##  Mean   :6.993   Mean   :15.8  
##  3rd Qu.:8.000   3rd Qu.:23.0  
##  Max.   :9.000   Max.   :31.0  
## 

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##    1.00   18.00   31.50   42.13   63.25  168.00      37

## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
##     Ozone Solar.R Wind Temp Month Day
## 1      41     190  7.4   67     5   1
## 2      36     118  8.0   72     5   2
## 3      12     149 12.6   74     5   3
## 4      18     313 11.5   62     5   4
## 5      NA      NA 14.3   56     5   5
## 6      28      NA 14.9   66     5   6
## 7      23     299  8.6   65     5   7
## 8      19      99 13.8   59     5   8
## 9       8      19 20.1   61     5   9
## 10     NA     194  8.6   69     5  10
## 11      7      NA  6.9   74     5  11
## 12     16     256  9.7   69     5  12
## 13     11     290  9.2   66     5  13
## 14     14     274 10.9   68     5  14
## 15     18      65 13.2   58     5  15
## 16     14     334 11.5   64     5  16
## 17     34     307 12.0   66     5  17
## 18      6      78 18.4   57     5  18
## 19     30     322 11.5   68     5  19
## 20     11      44  9.7   62     5  20
## 21      1       8  9.7   59     5  21
## 22     11     320 16.6   73     5  22
## 23      4      25  9.7   61     5  23
## 24     32      92 12.0   61     5  24
## 25     NA      66 16.6   57     5  25
## 26     NA     266 14.9   58     5  26
## 27     NA      NA  8.0   57     5  27
## 28     23      13 12.0   67     5  28
## 29     45     252 14.9   81     5  29
## 30    115     223  5.7   79     5  30
## 31     37     279  7.4   76     5  31
## 32     NA     286  8.6   78     6   1
## 33     NA     287  9.7   74     6   2
## 34     NA     242 16.1   67     6   3
## 35     NA     186  9.2   84     6   4
## 36     NA     220  8.6   85     6   5
## 37     NA     264 14.3   79     6   6
## 38     29     127  9.7   82     6   7
## 39     NA     273  6.9   87     6   8
## 40     71     291 13.8   90     6   9
## 41     39     323 11.5   87     6  10
## 42     NA     259 10.9   93     6  11
## 43     NA     250  9.2   92     6  12
## 44     23     148  8.0   82     6  13
## 45     NA     332 13.8   80     6  14
## 46     NA     322 11.5   79     6  15
## 47     21     191 14.9   77     6  16
## 48     37     284 20.7   72     6  17
## 49     20      37  9.2   65     6  18
## 50     12     120 11.5   73     6  19
## 51     13     137 10.3   76     6  20
## 52     NA     150  6.3   77     6  21
## 53     NA      59  1.7   76     6  22
## 54     NA      91  4.6   76     6  23
## 55     NA     250  6.3   76     6  24
## 56     NA     135  8.0   75     6  25
## 57     NA     127  8.0   78     6  26
## 58     NA      47 10.3   73     6  27
## 59     NA      98 11.5   80     6  28
## 60     NA      31 14.9   77     6  29
## 61     NA     138  8.0   83     6  30
## 62    135     269  4.1   84     7   1
## 63     49     248  9.2   85     7   2
## 64     32     236  9.2   81     7   3
## 65     NA     101 10.9   84     7   4
## 66     64     175  4.6   83     7   5
## 67     40     314 10.9   83     7   6
## 68     77     276  5.1   88     7   7
## 69     97     267  6.3   92     7   8
## 70     97     272  5.7   92     7   9
## 71     85     175  7.4   89     7  10
## 72     NA     139  8.6   82     7  11
## 73     10     264 14.3   73     7  12
## 74     27     175 14.9   81     7  13
## 75     NA     291 14.9   91     7  14
## 76      7      48 14.3   80     7  15
## 77     48     260  6.9   81     7  16
## 78     35     274 10.3   82     7  17
## 79     61     285  6.3   84     7  18
## 80     79     187  5.1   87     7  19
## 81     63     220 11.5   85     7  20
## 82     16       7  6.9   74     7  21
## 83     NA     258  9.7   81     7  22
## 84     NA     295 11.5   82     7  23
## 85     80     294  8.6   86     7  24
## 86    108     223  8.0   85     7  25
## 87     20      81  8.6   82     7  26
## 88     52      82 12.0   86     7  27
## 89     82     213  7.4   88     7  28
## 90     50     275  7.4   86     7  29
## 91     64     253  7.4   83     7  30
## 92     59     254  9.2   81     7  31
## 93     39      83  6.9   81     8   1
## 94      9      24 13.8   81     8   2
## 95     16      77  7.4   82     8   3
## 96     78      NA  6.9   86     8   4
## 97     35      NA  7.4   85     8   5
## 98     66      NA  4.6   87     8   6
## 99    122     255  4.0   89     8   7
## 100    89     229 10.3   90     8   8
## 101   110     207  8.0   90     8   9
## 102    NA     222  8.6   92     8  10
## 103    NA     137 11.5   86     8  11
## 104    44     192 11.5   86     8  12
## 105    28     273 11.5   82     8  13
## 106    65     157  9.7   80     8  14
## 107    NA      64 11.5   79     8  15
## 108    22      71 10.3   77     8  16
## 109    59      51  6.3   79     8  17
## 110    23     115  7.4   76     8  18
## 111    31     244 10.9   78     8  19
## 112    44     190 10.3   78     8  20
## 113    21     259 15.5   77     8  21
## 114     9      36 14.3   72     8  22
## 115    NA     255 12.6   75     8  23
## 116    45     212  9.7   79     8  24
## 117   168     238  3.4   81     8  25
## 118    73     215  8.0   86     8  26
## 119    NA     153  5.7   88     8  27
## 120    76     203  9.7   97     8  28
## 121   118     225  2.3   94     8  29
## 122    84     237  6.3   96     8  30
## 123    85     188  6.3   94     8  31
## 124    96     167  6.9   91     9   1
## 125    78     197  5.1   92     9   2
## 126    73     183  2.8   93     9   3
## 127    91     189  4.6   93     9   4
## 128    47      95  7.4   87     9   5
## 129    32      92 15.5   84     9   6
## 130    20     252 10.9   80     9   7
## 131    23     220 10.3   78     9   8
## 132    21     230 10.9   75     9   9
## 133    24     259  9.7   73     9  10
## 134    44     236 14.9   81     9  11
## 135    21     259 15.5   76     9  12
## 136    28     238  6.3   77     9  13
## 137     9      24 10.9   71     9  14
## 138    13     112 11.5   71     9  15
## 139    46     237  6.9   78     9  16
## 140    18     224 13.8   67     9  17
## 141    13      27 10.3   76     9  18
## 142    24     238 10.3   68     9  19
## 143    16     201  8.0   82     9  20
## 144    13     238 12.6   64     9  21
## 145    23      14  9.2   71     9  22
## 146    36     139 10.3   81     9  23
## 147     7      49 10.3   69     9  24
## 148    14      20 16.6   63     9  25
## 149    30     193  6.9   70     9  26
## 150    NA     145 13.2   77     9  27
## 151    14     191 14.3   75     9  28
## 152    18     131  8.0   76     9  29
## 153    20     223 11.5   68     9  30
  • Exemplo 1a
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##    1.00   11.00   18.00   23.62   31.50  115.00       5

*Exemplo 1b

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##    1.00   11.00   18.00   23.62   31.50  115.00       5

  • Boxplot using Formula
## [1] "formula"
  • Ex1

  • Ex2

## Error in eval(predvars, data, env): object 'Ozo' not found

  • Relacao entre variaveis
## 
## Call:
## lm(formula = Ozo ~ Wind, data = airquality)
## 
## Coefficients:
## (Intercept)         Wind  
##      96.873       -5.551

  • Multiplos Graficos

  • Plotly
  • Monta o gráfico e armazena em p
  • Exibe p
## Warning: Ignoring 37 observations
  • Lattice

Shiny App

Shiny applications not supported in static R Markdown documents

Distribution Types

## Error in shiny::shinyAppDir("dist"): No Shiny application exists at the path "dist"

Case Study

Proposal: I intend to show in the next lines the resolution of a problem presented in the book: Bussab,W.O. ; Morettin, P.A. Estatística Básica. São Paulo: 2017 Saraiva Educação.

Inference for various populations

A psychologist is investigating the relationship between the time it takes for an individual to react to a visual stimulus \((y)\) and some factors such as gender \((w)\), age \((x)\), and visual acuity (\(z\), measured as a percentage). The results were tabled, as follows:

Reaction time to a visual stimulus (y) and visual acuity (z) of 20 individuals, by sex (w) and age (x)
n y w x z
1 96 h 20 90
2 92 m 20 100
3 106 h 20 80
4 100 m 20 90
5 98 m 25 100
6 104 h 25 90
7 110 h 25 80
8 101 m 25 90
9 116 m 30 70
10 106 h 30 90
11 109 h 30 90
12 100 m 30 80
13 112 m 35 90
14 105 m 35 80
15 118 h 35 70
16 108 h 35 90
17 113 m 40 90
18 112 m 40 90
19 127 h 40 60
20 117 h 40 80
## [1] "We have the reaction time for n = 20 individuals. (values for random variable y)."
  • We observe we have two levels for the sex factor:
    • \(i = 1\): male (H)
    • \(i = 2\): female (M)
## [1] "n1 = n2 = 10"
  • The age factor has 5 levels:
    • \(i = 1\): individuals with 20 years old,
    • \(i = 2\): individuals with 25 years old,
    • \(i = 3\): individuals with 30 years old,
    • \(i = 4\): individuals with 35 years old,
    • \(i = 5\): individuals with 40 years old,
## [1] "n1 = n2 = n3 = n4 = n5 = 4"
  • Visual acuity as a percentage of complete vision also generates five levels:
    • \(i = 1\): individuals with 100% of acuity,
    • \(i = 2\): individuals with 90% of acuity,
    • \(i = 3\): individuals with 80% of acuity,
    • \(i = 4\): individuals with 70% of acuity,
    • \(i = 5\): individuals with 60% of acuity,
    • \(n_1 = 2, n_2 = 10, n_3 = 5, n_4 = 2, n_5 = 1\).

Therefore, it was not possible to control the variable \(z\) a priori as the other two, since it requires ophthalmic examinations for its measurement. Hence, the unbalance of the observed sizes. This factor is known as cofactor type.

  • Thus, for the sex factor, we have \(i = 1, 2, j = 1, 2, 3, ..., 10\), and for the age factor, the same model with \(i = 1, 2, ..., 5, j = 1, 2, 3, 4\).

Figure 1 shows the graphic model of this experiment:

Simple Linear Regression Model

A simple linear regression model can be represented as: \(y_i = α + βx_i + e_i,i = 1,2,...,n\)

The amount of information lost by the model or the sum of squares of errors (or deviations) is given by: \[SQ(α,β)= ∑ (e_i )^2 = ∑ (y_i-(α+ β∙x_i ))^2\]

To find the minimum value of SQ, we must derive SQ with respect to \(α\) and \(β\) and match the derivatives to zero, obtaining:

\[SQ_β= 2∙∑(y_i-α-β∙x_i )∙(-x_i ) = 0\] \[SQ_α= 2∙∑(y_i-α-β∙x_i )∙(-1) = 0\]

Solving this system of equations we get:

\[α ̂= (∑ y_i)/n- β ̂ (∑x_i )/n= y ̅- β ̂∙x ̅\] \[β ̂= (∑x_i y_i-((∑x_i )∙(∑y_i ))/n)/(∑x_i^2-(∑x_i )^2/n)= (∑x_i y_i-n(xy) ̅ /(∑x_i^2-nx ̅^2 )\]

Where, \(α ̂\) and \(β ̂\) are the estimated linear and angular coefficients, respectively.

In our Case Study, we assume:

\(y_i\): reaction time of i-th individual;
\(x_i\): age of i-th individual;
\(e_i\): deviation, $i = 1, 2, …, 20.

\(n = 20\),
\(∑y_i= 2150\),
\(∑i=600\),
\(∑x_i∙y_i=65400\),
\(y ̅=107.5\),
\(x ̅=30\),
\(∑x^2=1900\)

\[(β ) ̂=(65400- (20)(30)(107.5))/(19000-(20) (30)^2 )=0,90\] \[α ̂=107.5-(0,90)(30)=80,5\] What gives us the adjusted model: \[y ̂=80,5+0,9∙x_i,i=1,2,…,20\]

With this model, we can predict, for example, the average reaction time for 33-year-olds, which is an unobserved age group: \[y ̂(33)=80,5+0,9(33)=110,2.\]

The graph illustrated bellow adds to the previous one the line obtained by the calculated linear regression.